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GIFT   OF 

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LIBRARY 


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GEOMETRICAL 


STAIR    BUILDER, 


SIMPLIFIED. 


By    JOHN"     THOMAS. 


Entered  according  to  Act  of  Congress,  A.  D.  18B3, 

BY    JOHN    THOMAS, 
In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the  Northern  District  of  California. 

Any  infringement  on  the  copyright  of  this  book  will  be  prosecuted  to  the  utmost  extent  of  the  law. 

GIFT  OF 

Bancroft 
LIBRARY 


TOWNE  &  BACON,  BOOK  AND  JOB  PRINTKBS,  536  CLAY  STREET,  SAN  FKANCISCO. 


INTRODUCTION. 

THERE  has  been  so  much  said  and  written  on  the  art  of  Stair  Building  for  the  last  few 
years,  that  it  has  been  considered  as  bad  as  heresy  to  pretend  that  a  hand  rail  could  be 
got  up  without  the  use  of  prisms,  parallelograms,  ordinate  lines  and  tangent  boxes,  and 
a  host  of  lines  and  terms  accompanying  them ;  although  nine-tenths  of  the  mechanics  at 
the  sight  of  such  geometrical  problems  turned  from  them  in  disgust,  and  could  only 
know  what  they  heard  related  of  them.  Even  the  practical  Stair  Builder  had  to  bring 
his  book  along  with  him  to  his  shop,  like  a  school  boy,  for  fear  he  might  forget  one  of 
the  many  lines  given  therein — and  in  several  cases  they  are  entirely  wrong — and  then 
spend  half  a  day  at  what  this  work  teaches  to  do  in  ten  minutes  or  less.  Is  there  a  man 
that  will  go  to  the  trouble  to  set  out  and  make  two  moulds,  one  to  cut  his  stuff  by  and 
the  other  to  slide,  which  is  termed  a  slide  mould,  whilst  he  can  make  one  do ;  or  crack 
his  brain  studying  for  hours  over  any  of  the  preceding  works  on  Stair  Building,  whilst 
he  has  only  to  look  at  the  "  Geometrical  Stair  Builder  Simplified,"  which  teaches  him  to 
set  out  a  wreath  for  any  stairs  with  eight  or  ten  lines,  and  in  as  many  minutes. 

In  presenting  this  work  to  the  mechanic,  all  technicalities  and  high  sounding  phrases 
are  carefully  avoided,  so  that  any  man  can  understand  it.  For  simplicity  and  correct- 
ness it  cannot  be  equaled ;  for  quickness,  I  defy  the  world  to  beat  it,  unless  a  rail  can  be 
set  out  without  a  line,  or  done  by  magic. 


JOHN  THOMAS,, 

STAIR  BtriLDER'v •'  r-;  i  V 


SAN  FRANCISCO,  JANUARY,  1863. 


t 
'    , 


T»late    I. 

Fig.  1  is  a  quadrant ;  to  find  the  stretch  out  B  C  the  quadrant,  F  C  the  diameter, 
with  the  distance  F  C  in  the  compass,  describe  two  arcs,  cutting  each  other  at 
G,  and  draw  the  tangent  B  E  parallel  to  F  C,  cutting  the  quadrant  at  B ;  from  the 
point  G  draw  a  line  through  C,  cutting  the  tangent  at  D,  then  B  E  is  the  required 
length. 

Fig.  2,  another  method.  A  B  C  is  a  semicircle  ;  A  C  the  diameter,  with  the  distance 
A  C  as  a  radius ;  describe  two  arcs,  cutting  each  other  at  G,  draw  the  tangent  D  E 
through  B,  extended  parallel  to  A  C,  the  diameter ;  draw  the  lines  G  D  and  G  E 
through  the  points  A  and  C,  and  from  the  equilateral  triangle  D  E  G,  any  side  of  which 
is  equal  to  the  semicircle  ABC. 

Fig.  3  shows  the  method  of  setting  a  gauge  for  an  octagon  without  drawing  the  figure, 
the  square  being  given  from  P,  open  the  compass  to  O  the  center,  and  draw  the  arcs 
O  C,  then  C  is  the  point  to  set  the  gauge. 


The  attention  of  the  workman  is  called  to  Plate  II,  Fig.  A  and  Fig.  B  A.    The 
lengths  of  the  tangents  are  found  at  Fig.  B.  A.     From  the  base  line  1  8  the  perpendic- 
ular is  drawn  and  united  by  the  hypotenuse,  and  from  the  relative  positions  of  the  tan- 
gents to  the  perpendicular  and  hypotenuse  lines  the  spring  bevels  are  found.    To  apply 
.them  s^/J*late  III. 
..  ,'JWhen  th'fe,  taaigents  are  of  equal  length,  one  bevel  squares  both  ends. 

In  no  case  does  it  require  thicker  stuff  than  the  width  of  the  rail  to  get  out  a  wreath 
for  any  stairs. 


PL  ATP,   I. 


Fig.  3. 


(o 


PLAT  I;    L'. 


3 


OPlate    II. 

Fig.  A,  the  tangents,  is  at  obtuse  angles ;  1  2  8,  the  tangent  enclosing  the  center  line 
of  the  rail ;  1  8,  the  base  line  ;  8  3,  the  perpendicular.  Fig.  B  A  is  a  board  with  two 
gauge  lines  drawn  on  it  equal  in  width  to  one  of  the  tangents  at  1,  draw  a  line  at  right 
angles  to  1  3,  and  on  it  place  the  pitch  board,  the  point  resting  at  1,  and  where  the 
pitch  line  cuts  the  gauge  line  at  2,  then  2  1  is  the  length  of  the  bottom  tangent ;  from 

1  raise  up  to  3,  the  heighth  you  want  to  overcome,  and  draw  the  line  3  2,  which  is  the 
length  of  the  upper  tangent,  make  8  3,  Fig.  A,  equal  to  1  3  on  the  board,  and  draw  the 
hypotenuse  1  3,  then  make  1  2,  Fig.  A,  equal  to  1  2  on  the  board,  and  2  3,  Fig.  A,  equal 
to  2  3  on  the  board,  and  you  have  the  required  tangents,  and  when  placed  in  position 
with  two  pitches,  will  cover  exactly  the  tangents  1  2  8,  on  the  ground  plan,  to  find  the 
bevel  for  the  joint — joint  at  3 — set  one  leg  of  the  compass  in  3  and  open  it  to  2,  revolve 

2  round  to  7,  then  take  the  distance  1  2,  and  put  one  leg  in  8  and  cut  the  arcs  at  7 ; 
then  draw  the  line  7  3,  then  take  equal  distances  on  these  two  tangents  3  7,  3  2,  at  T  T ; 
then  square  down  to  J  J,  and  from  J  J  describe  two  arcs  cutting  each  other  at  M,  and 
draw  two  lines  from  this  point  to  J  J,  and  the  angle  formed  is  the  required  bevel  for 
the  joint  at  3.     To  find  the  bottom  bevel  for  the  joint  at  1,  reverse  the  bottom  tangents 
on  the  perpendicular  and  hypotenuse  lines,  as  shown  at  Fig.  B,  and  you  find  the  bevel 
in  the  same  manner  as  you  found  the  middle  bevel. 

Fig.  C  and  Fig.  D,  the  tangents  are  at  right  and  acute  angles.  Fig.  B  C  is  the  board 
for  Fig.  C,  Fig.  B  D  the  board  for  Fig.  D,  the  tangents  for  both  of  these  figures  are 
found  in  the  same  manner  as  for  Fig.  A.  The  dotted  lines  show  the  tangents  reversed, 
for  to  get  the  bottom  bevel,  the  tangents  and  bevels  for  all  rails  are  found  in  the  same 
manner  as  Figures  A  and  B. 


III. 

Fig.  A  shows  the  ground  plan  of  a  platform  stairs  with  the  risers  in  the  cylinder.  To 
draw  the  face  mould ;  128,.  the  tangents,  enclosing  the  center  line  of  the  rail,  1  8  the 
hase  line,  8  3  the  perpendicular.  Fig.  B  is  a  board  with  two  gauge  lines  equal  in  width 
to  one  of  the  tangents ;  at  4  draw  a  line  at  right  angles  to  4  3,  extended  hoth  ways  on 
this  line  place  the  pitch  board,  letting  the  point  5  project  beyond  the  line  4  3  the  same 
distance  as  from  1  to  5  Fig.  A ;  from  4  to  3  raise  up  the  height  of  one  riser  and  a  half, 
which  is  the  required  height,  then  draw  the  pitch  line  cutting  the  gauge  line  at  2,  and 
1  2  is  the  length  of  the  bottom  tangent ;  draw  the  line  from  3  to  2,  which  is  the  length 
of  the  top  tangent,  make  8  3  Fig.  A  equal  to  1  3. Fig.  B,  and  draw  the  hypotenuse  3  1, 
then  make  1  2  Fig.  A  equal  to  1  2  Fig.  B,  and  2  3  Fig.  A  equal  to  2  3  Fig.  B,  and  you 
have  the  required  tangents.  123,  when  placed  in  position  with  1  resting  in  1  on  the 
ground  plan,  2  3  will  exactly  cover  2  8  on  the  ground  plan.  The  bevel  for  the  joint  3 
is  shown  at  M,  and  the  bottom  bevel  is  found  by  reversing  the  tangents  on  the  perpen- 
dicular and  hypotenuse  lines  ;  with  a  bevel  transfer  the  tangents  123  Fig.  A  to  Fig.  P, 
the  board  you  cut  the  pattern  from,  intersect  the  tangents  by  dividing  each  into  eight 
equal  parts,  and  the  intersected  line  is  the  center  line  of  the  rail ;  with  half  the  width 
of  the  rail  in  the  compass,  put  one  leg  in  the  center  line  and  describe  arcs  on  each  side 
of  it,  which  gives  you  the  pattern — an  equal  width.  The  one  pattern  answers  for  the 
top  and  bottom  wreaths ;  the  joints  are  cut  at  right  angles  to  the  tangents,  and  square 
from  the  face  of  the  plank ;  the  bottom  bevel  is  applied  by  putting  the  stock  on  the 
face  of  the  wreath  at  1,  the  blade  passing  down  through  the  center  with  the  end  of  the 
stock  pointing  in  to  the  stairs ;  the  top  bevel  is  applied  reversed,  with  the  end  of  the 
stock  pointing  out  and  the  blade  passing  down  the  center ;  from  these  lines  square  the 
rail. 


PLATE  ,'i. 


Fig.  P. 


Fig.B 


1 K 


relate     IV. 

Fig.  A  is  the  ground  plan  of  a  platform  stairs  with  the  risers  at  the  springing  of  the 
cylinder.  To  draw  a  face  mould :  1  2  8  the  tangents  enclosing  the  center  line  of  the 
rail,  1  8  the  base  line,  8  3  the  perpendicular,  Fig.  B  the  board  with  the  two  gauge  lines 
equal  in  width  to  one  of  the  tangents ;  from  1  draw  a  line  at  right  angles  to  1  3,  and 
on  this  line  place  the  pitch  board,  the  point  resting  in  1 ,  as  you  require  to  raise  but  one 
riser  from  R  to  S ;  then  divide  the  heighth  of  the  riser  on  the  pitch  board  and  square 
over  to  3,  and  draw  the  lines  123,  which  is  the  required  length  of  the  tangents  ;  make 
8  3  Fig.  1  equal  to  1  3  Fig.  B,  and  draw  the  hypotenuse  1  3,  then  make  1  2  equal  to  1 
2  Fig.  B,  and  3  2  equal  to  3  2  Fig.  B,  1  2  3  are  the  tangents.  The  middle  bevel  is 
found  as  usual  at  M,  and  the  bottom  bevel  is  shown  at  Fig.  A  B  with  the  tangents 
reversed  on  the  perpendicular  and  hypotenuse  lines  with  the  bevel ;  transfer  the  tan- 
gents to  the  board  you  cut  your  pattern  from,  and  intersect  the  tangents  and  make  the 
pattern  as  usual,  leaving  some  stairwood  at  1  to  connect  with  the  straight  rail. 

Fig.  R  shows  the  second  flight  starting  from  a  level  landing  or  floor  round  a  cylinder 
to  flyers.  12845  the  tangents  enclosing  the  center  line  of  the  rail,  1  8  the  base  line, 
8  3  the  perpendicular,  Fig.  B  C  the  board  with  the  two  gauge  lines  from  1  to  5,  is  the 
required  heighth ;  1  2  the  pitch  line,  from  2  to  4  divide  into  two  equal  parts  and  square 
over  to  3  and  draw  the  lines  12345,  which  is  the  length  of  the  tangents  for  the 
upper  and  lower  wreaths  ;  make  8  3  Fig.  C  equal  to  1  3  Fig.  B  C,  and  draw  the  hypot- 
enuse 1  3  ;  make  1  2  equal  to  1  2  Fig.  B  C,  and  2  3  equal  to  2  3  Fig.  B  C,  1  2  3  are 
the  required  tangents  for  the  upper  wreath ;  extend  the  tangent  2  3  to  4,  and  make  4  3 
equal  to  3  2 ;  from  4  square  down  to  5,  and  make  5  4  equal  to  5  4  Fig.  B  C ;  transfer 
the  tangent  to  the  board  you  cut  the  pattern  from,  as  at  Plate  3,  Fig.  P.  The  bevels 
for  the  upper  wreath  are  found  as  usual ;  the  bevel  for  the  lower  wreath  at  the  joint  5, 
is  shown  at  3  Fig.  B  C.  The  lower  wreath  can  be  set  out  by  the  compass,  as  the  tan- 
gents are  nearly  equal  in  length. 


I^late 

A  shows  the  ground  plan  of  a  geometrical  'staircase  with  winders  round  the  semicircle. 
Fig.  B  shows  the  manner  of  setting  out  the  face  string  before  it  is  bent  round  the  drum. 
It  is  generally  one  and  a  half  inches  thick,  cut  out  in  the  center  as  shown  at  V  Y.  The 
yeneer,  which  is  equal  to  the  stretch  out  of  the  semicircle  ABC,  W  W  the  winders, 
G  G  the  graduating  steps,  F  F  the  flyers,  P  P  the  splices.  If  you  want  to  raise  the 
rail  so  that  the  long  bannister  goes  over  the  cylinder,  you  must  not  have  a  graduating 
step  on  the  lower  part  of  the  cylinder,  but  put  a  winder  in  the  place  of  a  graduating 
step  between  the  springing  and  the  flyers ;  on  the  upper  portion  of  the  cylinder  put  a 
winder  in  place  of  the  graduating  step,  and  one  graduating  step  between  it  and  the 
flyers,  in  order  to  give  room  to  form  an  easing  between  the  upper  wreath  and  the 
straight  rail.  To  form  the  upper  and  lower  easing  you  set  out  an  elevation  of  the  flyers 
and  winders,  and  the  angle  formed  between  is  the  place  to  make  the  casings,  as  shown 
at  Plate  9.  If  the  face  string  is  to  be  moulded,  gauge  the  width  of  the  opening  on  the 
string  before  bending  it ;  and  when  bent,  cut  it  off  and  set  it  back  the  required  depth 
for  the  moulding,  and  then  plant  in  the  moulding,  which  will  hide  the  saw  kerf. 


PLAT  I: 


Fiq  A 


Fiy.B 


Fig.  P. 


I»late 

Shows  the  method  of  drawing  the  face  mould  for  the  geometrical  staircase  shown  at 
Plate  5.  With  the  short  bannisters  over  the  winders,  enclose  the  center  line  of  the  rail, 
as  usual,  with  the  tangents  I  2  8  on  the  ground  plan ;  Fig.  A,  8  1  the  base  line,  8  3  the 
perpendicular ;  Fig.  B  the  board  with  the  two  gauge  lines  equal  in  width  to  one  of  the 
tangents  on  the  line  1  4 ;  place  the  pitch  board  and  draw  the  pitch  line  1  2,  and  from 
4  raise  up  to  L,  the  number  of  risers  in  the  cylinder ;  divide  it  in  two  equal  parts, 
squaring  over  to  3,  and  draw  the  line  3  2 ;  make  8  3  Fig.  A  equal  to  1  3  Fig.  B,  and 
draw  the  hypotenuse  1  3  ;  make  1  2  equal  to  1  2  Fig.  B,  and  2  3  equal  to  2  3  Fig.  B, 
and  123  are  the  required  tangents.  Transfer  them  to  Fig.  P,  the  board  you  cut  the 
pattern  from,  and  proceed  as  usual  with  the  formation  of  the  mould.  The  one  pattern 
answers  for  the  upper  and  lower  wreaths.  The  bevels  for  both  ends  are  found  as  usual 
in  all  cases. 


Fig.  A  is  the  ground  plan  of  a  staircase,  the  lower  part  constructed  of  flyers,  with 
winders  round  the  semicircle  to  land  on  a  level  floor.  Fig.  B  the  face  string  without  a 
graduating  step.  Fig.  C  the  rail,  the  lower  wreath  forming  a  perfect  easing  over  the 
flyers,  L  the  landing,  with  the  rail  raised  four  inches  over  it,  so  that  the  long  bannisters 
can  go  on  the  landing.  E  E  Fig.  B,  the  easings  of  the  cylinder ;  P  the  splice  to  con- 
nect with  the  face  string. 


PLATE  7. 


. 


W<ATT:  a. 


HPlate 

Shows  the  manner  of  getting  the  face  mould  for  the  stairs  Plate  7.  12845  Fig.  A, 
the  tangents  enclosing  the  center  line  of  the  rail ;  1  8  the  hase  line  ;  8  3  the  perpendic- 
ular. Fig.  B  a  hoard  with  two  gauge  lines  equal  in  width  to  one  of  the  tangents ;  from 
the  line  1  3  square  over  to  4,  and  on  it  place  the  pitch  hoard  from  4  to  L,  the  heighth 
of  four  risers,  and  four  inches  from  where  the  pitch  line  cuts  the  gauge  line  at  2,  divide 
from  2  to  L  in  two  equal  parts  and  square  over  to  3,  then  draw  the  line  2  3,  and  make 
8  3  Fig.  A  equal  to  1  3  Fig.  B,  and  draw  the  hypotenuse  1  3 ;  make  1  2  Fig.  A  equal 
to  1  2  Fig.  B,  and  2  3  equal  to  2  3  Fig.  B,  and  draw  the  tangents  1  2  3  to  form  the 
upper  wreath ;  extend  the  tangent  2  3  to  4,  and  make  3  4  equal  to  3  2 ;  from  4  square 
down  to  5,  and  make  4  5  equal  to  4  5  on  the  ground  plan.  Transfer  the  tangents  as 
usual,  and  form  the  pattern,  leaving  ahout  three  inches  of  straight  wood  on  the  upper 
wreath  at  5.  The  bevels  for  the  lower  wreath  are  found  as  usual ;  the  bevel  for  the  top 
wreath  is  shown  at  T  Fig.  B. 


JPlate    IX. 

Fig.  A  shows  the  ground  plan  of  a  staircase,  the  lower  part  of  which  is  constructed 
of  flyers  with  winders  round  the  semicircle  to  land  on  a  level  floor. 

Fig.  B  the  face  string ;  W  the  winders,  with  one  winder  in  the  place  of  a  graduating 
step,  in  order  to  raise  the  rail  so  that  the  long  bannisters  can  go  round  the  cylinder. 

Fig  C  the  rail,  with  the  center  line  raised  up  four  inches  from  the  corner  of  the  step 
and  riser,  which  gives  a  most  graceful  easing  at  E ;  if  there  was  a  graduating  with  the 
winder,  it  would  make  the  easing  too  long  and  too  far  from  the  curve  of  the  rail  as  it 
passes  round  the  cylinder.  If  you  want  to  put  the  short  bannisters  over  the  winders, 
you  can  do  it  on  this  plan ;  but  it  would  be  better  to  put  in  two  graduating  steps,  and 
by  so  doing  you  produce  the  same  easing  as  shown  at  E. 


PLATE   !). 


PLATE   If i. 


fig.  P 


To  draw  the  face  mould  of  the  hand-rail  of  the  stairs,  as  shown  at  Plate  IX.  128 
4  5  Fig.  A,  the  tangents  enclosing  the  center  line  of  the  rail ;  1  8  the  base  line  ;  8  3  the 
perpendicular.  Fig.  B  the  board,  1  4  the  gauge  lines,  4  L  the  heighth  of  four  risers, 
123  the  length  of  the  tangents ;  transfer  those  tangents  to  Fig.  A  as  usual,  12345 
Fig.  A  are  the  tangents. 

The  middle  bevel  for  the  joint  at  3  is  shown  at  M  ;  the  bottom  bevel  for  the  joint  at 
1  is  found  as  usual  by  reversing  the  tangents.  The  bevel  for  the  upper  wreath  is  shown 
at  the  angle  T  Fig.  B. 


relate     XI. 

To  draw  the  face  mould  for  a  staircase  with  winders,  landing  the  well  hole,  formed  by 
two  quadrants  of  unequal  radii.  12845  Fig.  A,  the  tangents  enclosing  the  center  line  of 

• 

the  radii ;  1  8  the  base  line  ;  8  3  the  perpendicular ;  Fig.  B  tlio  board  with  three  gauge  lines 
equal  in  width  to  4  8  8  2  Fig.  A.  From  L  square  over  to  D,  and  on  this  line  place  the 
graduating  step  with  the  point  resting  at  1 ;  then  draw  the  pitch  line  to  2,  which  is  from 
1  to  2,  the  length  of  the  bottom  tangent  for  the  lower  wreath ;  from  L  raise  up  the 
heighth  of  four  risers  and  four  inches,  then  draw  the  line  4  2  through.  3,  and  3  2  is  the 
length  of  the  top  tangent  of  the  lower  wreath,  and  3  4  the  length  of  the  bottom  tan- 
gent of  the  upper  wreath ;  make  8  3  Fig.  A  equal  to  1  3  Fig.  B,  and  draw  the  hypote- 
nuse ;  make  1  2  equal  to  1  2  Fig.  B,  and  2  3  equal  to  2  3  Fig.  B.  To  form  the  upper 
wreath,  extend  the  tangent  3  2  to  4,  and  make  4  3  equal  to  4  3  Fig,  B ;  from  4  square 
over  to  5,  and  make  4  5  equal  to  4  5  on  the  ground  plan  Fig.  A.  The  bevel  for  the 
joint  3  is  shown  at  M ;  the  bottom  bevel  is  found  as  usual.  The  bevel  for  the  upper 
wreath  is  shown  at  T  Fig.  B. 


PLATE   It. 


XII. 

• 

To  draw  the  face  mould  for  a  quarter  circle  rectangular  stairs.  128  Fig.  A,  the  tan- 
gents enclosing  the  center  line  of  the  rail ;  1  8  the  base  line ;  8  3  the  perpendicular, 
which  is' equal  in  heighth  to  four  risers  ;  1  3  the  hypotenuse  ;  Fig.  B  the  board  with  the 
two  gauge  lines  equal  in  width  to  one  of  the  tangents.  From  4  to  L,  the  heighth  of  four 
risers,  divide  that  line  into  two  equal  parts  at  2,  and  draw  the  lines  1  2  and  2  3,  which 
is  an  equal  length  with  the  distance  1  2  Fig.  B  in  the  compass ;  put  one  leg  in  1  Fig.  A, 
and  describe  the  arcs  at  2,  then  change  the  compass  from  1  to  3  and  cut  the  arcs  at  2, 
and  draw  the  tangents  1  2  2  3,  as  they  are  an  equal  length,  the  bevel  B  will  square  both 
ends. 

REMARK. — At  the  time  of  building  the  stairs,  set  out  the  tangents  on  the  board  Fig. 
B,  in  order  to  have  the  tangents  an  equal  length,  and  for  them  to  come  parallel  to  the 
pitch  line  of  the  graduating  step.  From  4  to  R,  the  heighth  of  one  riser,  square  over 
to  O,  then  draw  O  W  parallel  to  R  4,  and  from  1  to  "W  is  the  width  of  the  graduating 
step.  If  the  stairs  should  be  built,  extend  the  tangent  2  1  down  until  it  cuts  the  pitch 
line  of  the  flyers;  the  same  with  the  tangent  2  3,  and  the  angles  formed  will  be  the 
casings. 


XXIX. 

• 

The  ground  plan  of  a  staircase  with  winders  round  the  quarter  circle,  starting  from  a 
newel  and  miter  cap  to  draw  the  face  mould  in  one  piece  with  a  perfect  easing  at  the 
newel  cap.  12834  the  tangents  enclosing  the  center  line  of  the  rail ;  4  8  the  base 
line  of  Fig.  B ;  8  3  the  perpendicular ;  Fig.  B  A  the  board  with  the  two  gauge  lines ; 
G  the  graduating  step,  with  the  point  resting  at  4.  From  4  to  L  raise  up  the  heighth 
of  three  risers  and  two  inches,  which  is  the  required  heighth  from  the  bottom  of  the 
newel  cap  to  the  center  of  the  rail  at  4  Fig.  B,  where  the  pitch  line  cuts  the  gauge  line 
at  5.  From  5  to  L  divide  in  two  equal  parts  at  O,  square  over  to  3  and  draw  the  line 
354,  wrhich  is  the  length  of  the  tangents  for  Fig.  B ;  make  the  perpendicular  8  3  Fig. 
B  equal  to  4  3  Fig.  B  A,  and  draw  the  hypotenuse  3  4 ;  transfer  the  tangents  as  usual, 
453  Fig.  B  A  to  4  5  3  Fig.  B ;  1  8  the  base  line  for  Fig.  A ;  8  3  the  perpendicular, 
equal  in  heighth  to  O  L  Fig.  B  A ;  make  3  2  equal  to  3  5  Fig.  B,  and  1  2  equal  to  1  2 
on  the  ground  plan.  With  the  bevel  transfer  the  tangents  of  the  upper  half  of  the 
wreath  to  the  board  you  cut  the  pattern  from,  as  shown  at  Fig.  P ;  then  transfer  the 
tangents  of  Fig.  A  to  the  same  board  and  unite  the  two — 3  3,  keeping  the  lines  3  5  and 
3  2  on  a  straight  line  ;  intersect  them  as  shown,  and  when  in  position  with  1  2,  covering 
1  2  on  the  ground  plan,  2335  will  exactly  cover  2  8  3  on  the  ground  plan,  and  5  4 
will  exactly  cover  3  4.  Also  having  the  pitch  of  the  graduating  step  G,  always  leave  a 
few  inches  of  straight  wood  at  4  and  at  1,  for  the  purpose  of  squaring  up  from  the  bot- 
tom to  make  the  miter  for  the  newel  cap.  The  bevel  for  the  joint  at  the  newel  cap  is 
shown  at  B  Fig.  B  A.  The  bevel  for  the  center  of  the  wreath  3  3  is  shown  at  M  ;  and 
to  find  the  bevel  for  the  joint  at  4,  you  reverse,  as  usual,  the  tangents  of  Fig.  B,  then 
you  have  three  points  to  square  the  a  il  from. 


PLAT.K  73. 


PLATE   Ik. 


A    G     \ 


Flate 

To  draw  the  face  mould  for  a  hand  rail  over  winders.  The  ground  plan  is  formed  by 
the  quadrant  of  a  given  radius,  with  the  arcs  of  a  circle  added  by  a  smaller  radius,  start- 
ing from  a  newel  and  miter  cap. 

It  is  useless  to  describe  this  drawing,  for  it  would  be  only  a  repetition  of  Plate  XIII, 
and  all  former  plates.  You  see  that  the  principle  is  the  same,  and  that  they  are  num- 
bered alike ;  the  only  difference  is  the  arcs  of  a  circle  added.  Bear  in  mind  that  the 
wreath,  starting  from  the  newel  cap  at  Plates  XIX  and  XXI,  is  just  the  same  as  this, 
and  the  wreaths  landing  are  the  same  as  in  Plate  XV. 


T»late 

Shows  the  ground  plan  of  a  staircase  with  winders  round  the  quarter  circle,  landing 
on  a  level  floor.  To  draw  the  face  mould  for  the  wreath  over  the  winders  and  the  eas- 
ing over  the  landing  at  L  in  one  piece,  with  the  long  bannisters  over  the  winders  :  1  2  8 

3  4  the  tangents  enclosing  the  center  line  of  the  rail ;  1  8  the  base  line  for  Fig.  A ;  8  3 
the  perpendicular ;  Fig.  B  A  the  board  with  the  two  gauge  lines,  equal  in  width  to  one 
of  the  tangents.    From  1  to  4  square  over,  and  on  this  line  place  the  pitch  board  of  the 
winders  G,  the  point  resting  in  1,  and  draw  the  pitch  line,  cutting  the  gauge  line  at  2. 

• 

From  4  raise  up  to  L  the  heighth  of  four  risers ;  from  2  to  L  divide  in  two  equal  parts, 
square  over  to  3,  then  draw  the  line  3  2,  and  you  have  the  tangents  for  the  lower  wreath. 

4  3  the  base  line  of  Fig.  B,  4  5  the  perpendicular ;  then  make  3  4  equal  to  2  3  Fig. 
B  A,  and  make  4  5  equal  to  3  4  on  the  ground  plan ;  unite  the  tangents  as  at  Plate 
XIII  to  cut  your  pattern.    The  tangent  1  2  Fig.  P,  when  placed  in  position,  will  exactly 
cover  1  2  on  the  ground  plan,  and  2  4  will  cover  2  3 ;  and  4  8  will  be  perfectly  level, 
covering  3  4  on  the  ground  plan.     The  bevel  for  the  joint  at  5  is  shown  as  usual  at  T 
Fig.  B  A.     The  bevel  for  the  center  at  3  3,  is  shown  as  usual  at  M.     The  bottom  bevel 
is  found  by  reversing  the  tangents  of  Fig.  A. 


PLATE  15. 


PLATE  16 


.  H. 


To  construct  the  face  mould  for  a  hand  rail,  starting  from  a  newel  with  a  miter  cap, 
the  ground  plan  being  either  an  elliptic  curve  or  the  arc  of  a  circle.  To  find  the  position 
of  the  tangents  on  the  ground  plan :  Fig.  C  the  pitch  board  from  1  to  5  is  six  inches,  the 
heighth  of  the  center  of  the  newel  cap  from  the  first  step  ;  from  5  square  over  to  3,  then 
draw  the  tangent  8  2  Fig.  A,  extended ;  at  8  place  the  point  of  the  pitch  board ;  from 
the  pitch  board  at  6  to  2,  make  it  equal  to  5  3  Fig.  C,  and  from  the  miter  cap  draw 
the  tangent  1  2  ;  from  2  square  up  to  7,  and  where  the  pitch  line  cuts  at  7,  from  7  to 
8  is  the  length  of  the  tangent.  On  the  base  line  1  8  erect  the  perpendicular  8  3,  and 
make  it  equal  to  7  2  ;  then  make  3  2  equal  to  7  8,  and  1  2  equal  to  1  2  on  the  ground 
plan,  and  you  have  the  required  tangents ;  and  when  placed  in  position,  with  1  2  rest- 
ing on  1  2  on  the  ground  plan,  3  will  exactly  cover  8,  and  the  tangent  2  3  will  have  the 
pitch  of  the  flyers.  The  bevel  for  the  bottom  is  shown  at  B ;  the  bevel  for  the  top  is 
shown  at  S. 

Always  leave  a  few  inches  of  straight  wood  at  joint  1  to  square  up  to  form. 'the  miter 
for  the  cap. 


Shows  the  face  string  with  the  easing  E,  the  pannel  P,  and  also  the  best  manner  of 
putting  the  step  and  risers  together,  B  B.  The  blocking  and  the  risers  should  be 
screwed  from  the  back  to  the  step,  and  the  blocking  glued  and  nailed.  Fig.  A  shows 
the  manner  of  setting  out  the  length  of  the  rail  at  the  newel  cap  ;  and  to  find  the  miter 
of  the  rail  for  the  cap,  from  the  top  of  the  step  to  the  center  of  the  rail  should  be  six 
inches,  and  the  center  of  the  straight  rail  cutting  through  the  corner  of  the  steps  and 
risers  at  C  ;  the  center  of  the  newel  projecting  three -fourths  of  an  inch  outside  the  face 
of  the  first  riser,  so  that  you  may  have  a  longer  easing  at  D.  Fig.  B  shows  the  board 
you  cut  the  miter  of  the  newel  cap  in ;  T  T  are  two  cuts  in  the  board  equal  to  the 
width  of  the  rail,  with  a  screw  in  the  center  to  fasten  the  cap  to  it.  Mark  the  width 
of  the  rail  on  the  cap,  and  bring  one  of  these  marks  opposite  the  cut  T ;  cut  the  miter 
half  way  and  turn  the  cap  round  until  the  other  mark  is  opposite  the  other  cut  T,  thei 

• 

cut  the  miter  through  and  you  have  it  correct  from  the  saw. 


PL  ATM  77. 


AV. 


Ftq.B 


w 


T»late 

Fig.  A  is  the  plan  of  a  staircase  with  the  tangents  on  the  ground  plan  at  acute  angles. 
It  also  shows  that  no  matter  in  what  position  the  tangents  on  the  ground  plan  are  placed, 
iccording  to  this  system,  the  difficulties  in  stair  railing  can  be  overcome  by  the  few  sim- 
ple lines  laid  down  in  this  work.  It  is  useless  to  describe  this  Plate,  as  it  would  only 
3nter  into  a  repetition  of  Plate  XII. 


JPlate     XIX. 

Exhibits  the  ground  plan  of  an  elliptical  staircase.     To  find  the  face  mould :  1  2  3 

the  tangents  enclosing  Fig.  A ;  3  4  5  the  tangents  enclosing  the  center  line  of  the  rail 

Fig.  B ;  5  6  7  enclosing  the  center  line  at  Fig.  C ;  7  8  9  at  Fig.  E,  and  9  10  11  Fig.  F; 

5  7  the  base  line  of  Fig.  C ;  7  7  the  perpendicular ;  Fig.  C  C  the  board  with  the  twri 

gauge  lines ;  7  6  and  11  12  equal  in  width  to  one  of  the  tangents.    On  line  7  6  raise  up 

the  heighth  of  the  number  of  risers  that  the  base  line  5  7  covers ;  divide  it  in  two 

equal  parts  and  square  over  to  5,  and  draw  the  lines  7556,  which  is  the  length  of  the 

tangents  for  Fig.  C  ;  make  the  perpendicular  7  7  Fig.  C  equal  to  7  6  Fig.  C  C,  and  draw 

the  hypotenuse  7  5 ;  make  5  6  Fig.  C  equal  to  7  5  Fig.  C  C,  and  6  7  equal  to  5  6,  th< 

tangents  567  will  cover  the  corresponding  figures  on  the  ground  plan.     From  the  tan 

gents  Fig.  C  C  you  find  the  pitch  for  the  lower  wreath  Fig.  B  and  Fig.  A,  and  also  for 

the  wreath  Figs.  E  and  F ;  from  the  gauge  line  11  12  Fig.  C  C,  draw  the  line  8  9  equal 

in  width  to  the  tangent  5  4  Fig.  B,  then  continue  the  tangent  6  5  to  cut  the  line  8  9  at 

4  Fig.  A  B.     From  5  set  down  the  heighth  from  the  newel  cap  to  the  tangent  5  Fig.  B, 

then  square  over  to  8  and  divide  the  line  8  4  in  two  equal  parts,  and  square  over  to  2J 

and  draw  the  lines  8  2  and  2  4  and  4  5,  which  is  the  length  of  the  tangents  for  t1 

lower  wreath  ;  5  3  the  base  line  Fig.  B  ;  3  8  the  perpendicular,  equal  to  2  5  Fig.  A  B 

and  make  5  4  equal  to  5  4  Fig.  A  B,  and  4  8  equal  to  4  2,  then  5  4  8  is  the  tangent  fo: 

the  wreath  Fig.  B ;  1  3  the  base  line  Fig.  A ;  3  8  the  perpendicular,  epual  to  1  2  Fig 

A  B,  and  2  8  equal  to  2  8  Fig.  A  B,  and  1  2  equal  to  1  2  on  the  ground  plan.     On  tb 

board  you  cut  the  pattern  from,  unite  the  tangents  as  usual,  as  shown  at  Fig.  A  B,  Pla 

XX,  which  is  the  wreath  to  cover  from  the  newel  cap  to  the  tangent  5  Fig.  B.     Th 

length  of  the  tangents  for  the  upper  wreath  are  found  on  the  board  Fig.  E  F ;  7  A 

is  equal  to  the  pitch  of  the  tangent  5  7  Fig.  C  C.     From  7  to  C  is  five  risers  and  four 

inches.     To  raise  the  rail  on  the  landing,  from  A  to  C  divide  in  two  equal  parts  and 

square  over  to  B,  and  draw  the  line  C  B  B  A,  and  you  have  the  required  length  of  the 

tangents  for  the  wreaths  Figs.  E  and  F,  which  are  numbered  7  A  B  and  BCD.     Th© 

bevel  for  the  joint  D  is  shown  at  T  Fig.  E  F  ;  and  the  bevel  for  joint  1  at  the  newel  cap 

is  shown  at  A  Fig.  A  B.     The  other  bevels  are  found  as  usual.     Plate  XX  shows  the 

patterns. 


PLATE -fd 


PLATE    •> 


Fig.  C. 


D 


Fig. 


E.F. 


PLATE  2 


XX. 


The  ground  plan  of  a  circular  staircase.     Enclose  the  center  line  of  the  rail  with  the 

tangents  123,345,667,789.91011.     It  is  useless  to  describe  this  rail,  as  it  would 

• 
be  only  a  repetition  of  Plate  XIX.     Although  Plate  XIX  is  elliptical  and  this  circular, 

still  the  principle  is  the  same  ;  and  as  this  Plate  and  Plate  XIX  are  numbered  alike,  you 
can  read  the  instruction  for  Plate  XIX,  and  you  will  find  the  wreaths.  Figures  A  B,  C  C 
and  E  F  are  the  boards,  to  find  the  lengths  of  the  tangents. 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
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This  book  is  DUE  on  the  last  date  stamped  below. 


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LD  21-100m-ll,'49(B7146sl6)476 


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